A concrete patio is 5 (2)/(3) feet wide. It has an area of 36 (2)/(3) square feet. is the concrete slab long enough to fit a 7-foot picnic table without placing the table along …

Question

A concrete patio is


`5 (2)/(3)`
feet wide. It has an area of

`36 (2)/(3)`
square feet. is the concrete slab long enough to fit a 7-foot picnic table without placing the table along the diagonal of the patio? Explain. ​

Answer 1

The length of concrete patio is 6.5 feet which is less than given 7 foot picnic table. So the concrete slab is not enough to fit a 7 foot picnic table

Solution:

Given that concrete patio is
`5(2)/(3)` feet wide

Area of concrete patio =
`36(2)/(3)` square feet

Therefore,

`\texttt{Width of concrete patio = }5(2)/(3)=(5* 3+2)/(3)=(17)/(3)feet\\\\\text{Area of concrete patio = }36(2)/(3)=(36* 3+2)/(3)=(110)/(3)feet^2`

Let us find the length of concrete patio

Concrete patio is usually of shape rectangle

Area of concrete patio = length x width

`(110)/(3) = length * (17)/(3)\\\\length = (110)/(3) * (3)/(17)\\\\length = (110)/(17) = 6.4705 \approx 6.5`

Therefore length of concrete patio is 6.5 feet

So it cannot fit the 7 foot picnic table. Since the length of concrete patio is 6.5 feet which is less than given 7 foot picnic table